Let (H, α) be a Hom-Hopf algebra and (A, β) be a Hom-algebra. In this paper we will construct the Hom-crossed product (A# σ H, β ⊗ α), and prove that the extension A ⊆ A# σ H is actually a Hom-type cleft extension and vice versa. Then we will give the necessary and sufficient conditions to make (A# σ H, β ⊗ α) into a Hom-Hopf algebra. Finally we will study the lazy 2-cocycle on (H, α).